Title: The Ramsey numbers for disjoint unions of trees
Abstract: For given graphs G and H, the Ramsey number R(G,H) is the smallest natural number n such that for every graph F of order n: either F contains G or the complement of F contains H. In this paper, we investigate the Ramsey number R(∪G,H), where G is a tree and H is a wheel Wm or a complete graph Km. We show that if n⩾3, then R(kSn,W4)=(k+1)n for k⩾2, even n and R(kSn,W4)=(k+1)n-1 for k⩾1 and odd n. We also show that R(⋃i=1kTni,Km)=R(Tnk,Km)+∑i=1k-1ni.
Publication Year: 2006
Publication Date: 2006-12-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 15
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot